Prior art in the area of firearms is of a single type, that of a shock absorber. Operation of a gun shock-absorbing system requires that all or part of the gun move, in response to the recoil force. That part of the gun that moves is then decelerated, as slowly as possible, by the shock-absorbing system. Normally the shock absorber is some form of a spring-damping system interposed between the gun and its supporting structure. Its function is primarily to reduce the maximum amplitude and the shock-like characteristics of the force transmitted to the supporting structure. For example, in the case of a pistol, Porter (U.S. Pat. No. 2,522,192) shows that a slider moves rearward, in response to the recoil force, and is decelerated by a spring between the slider and the butt of the pistol. In Mathiew (U.S. Pat. No. 2,731,753), a rifle moves rearward and is declerated by springs contained in the stock, which compress against the shooter's shoulder. In Nasypany (U.S. Pat. No. 4,088,057), part of the recoil force is directly transmitted, by gun motion, to the shooter's shoulder while a part is transferred to an auxiliary mass. This auxiliary mass is accelerated rearward by a portion of the gun gases and, in turn, is slowly decelerated by the spring-like action of the compressibility of a trapped gas. In Edwards (U.S. Pat. No. 4,279,091), the rearward motion of the gun compresses a spring, in the stock of the gun, which, in turn, initiates rearward motion of an auxiliary mass. The rearward motion of the auxiliary mass is then slowly decelerated by a second spring.
These inventions are all variations on the simple and well-known shock absorber. Shock absorbers have been in use with machine guns since World War II. In the application of this invention to firearms, however, it is an objective of the invention to reduce gun motion as nearly as possible to zero. With no gun motion, a simple shock absorber does not function. Thus, prior art in the area of firearms (i.e. shock absorbers) does not teach the art disclosed in this invention.
There is also related prior art in the area of vibration isolation and damping, related to various commercial applications. Some of the prior art in this area again involves the shock absorber concept. For example, Karnopp (U.S. Pat. No. 3,807,678) shows a simple spring-damping system (in which the magnitude of the damping can be controlled), used to minimize transmission of a vibration (a motion of a mass) from the mass to its supporting structure. Again the mass must be in motion for the spring-damping system to perform its function. A vibration, however, can usually be described as a sinusoidal motion, predominantly at a single frequency. The spring-mass-damping system must then be tuned, as in Karnopp, to be anti-resonant at the vibration driving frequency. As in the prior art related to firearms, a vibration damping system such as that shown by Karnopp exerts no balancing forces, in fact does not function, unless there is relative motion between the primary mass and its supporting structure. This art, therefore, also does not teach the art disclosed in this invention.
Finally, a second type of vibration isolator shown in the prior art is the so-called dynamic damper. Such a system was first analyzed by Ormondroyd and Den Hartog in 1928 (Reference 1) and applications of the dynamic damper appear in the prior art in, for example, Settles (U.S, Pat. No. 2,875,731) and in Flannelly (U.S. Pat. No. 3,322,379) in 1959 and 1967, respectively. Detailed analyses of dynamic dampers are shown in textbooks on structural vibrations, for example, in Timoshenko (Reference 2), as early as 1928. The major difference between the dynamic damper and the more common shock absorber approach to vibration isolation is that the dynamic damper reduces transmission of vibrations by reducing the vibration, or motion, of the vibration source. If there is no vibration of the primary mass, no vibration can be transmitted to its supporting structure. In a dynamic damper the forces which cause vibration are transferred to an auxiliary spring-mass system. The auxiliary mass then performs strong vibrations but, since motion of the primary mass has been virtually eliminated, little or no vibration is transmitted to the main support structure.
FIG. 1 shows a schematic of a simple dynamic damper, an example taken from Reference 2. In this example, the rotating motor is assumed to be unbalanced, and transmits a sinusoidal force to the beam (supporting structure) which supports the motor, at the frequency of rotation of the motor. In this application the auxiliary spring-mass system is tuned to the frequency of the driving force, the motor rotational speed. The auxiliary mass performs strong displacement oscillations while the motor and its supporting beam remain virtually motionless. The analysis of the system shown in FIG. 1, from Reference 2, shows that the motion of the system can be represented by two simultaneous second-order differential equations, involving two degrees of freedom. The analysis also shows that there is indeed a solution for this system in which the source of the oscillatory driving force (the motor) and its supporting structure (the beam) remain virtually motionless.
As clearly pointed out in Settles (U.S. Pat. No. 2,875,731) the dynamic damper works because the auxiliary mass moves at the same frequency as the driving force, with a phase lag of 180.degree., and provides an auxiliary force which is at all times of equal magnitude to, but in the opposite direction from, the driving force. Thus the driving force is at all times exactly carcelled out and there is no net force remaining to cause motion in the vibration source. However, such a dynamic damper cannot be built to provide this continuous force cancellation if the driving force-time characteristic is significantly different from sinusoidal. A fundamental characteristic of a simple spring-mass system attached to a support is a varying force on the support which is sinusoidal in character, at a single frequency. If a driving force is not sinusoidal, and therefore can be represented by the sum of a number of sinusoidal oscillations at different frequencies (a Fourier representation), then a simple spring-mass system, a dynamic damper, cannot be designed to exactly, or even approximately, cancel out the driving force at all times. A dynamic damper can be designed to cancel out vibrations at one of these frequencies, but vibrations at all other frequencies will remain.
A unidirectional, impulse-type driving force, such as is generated in firing a gun, or in the contact of a jack hammer or sand tamper tool with the ground, is the most extreme example of this mismatch. FIGS. 2 and 3 show example force-time traces of a dynamic damper applied to a sinusoidal driving force (FIG. 2) and to a unidirectional, impulse-type force (FIG. 3). FIG. 2 shows the force generated by the dynamic damper at all times of equal magnitude to, and 180.degree. out of phase from, the driving force, with the result that the net force is at all times equal to zero. FIG. 3, however, shows that the force generated by the dynamic damper can, during the period of the impulse, exactly cancel out the driving force, but at all other times the dynamic damper continues to provide a sinusoidal force which is unopposed by the driving force. Particularly because the spring-mass system of the dynamic damper provides both positive and negative forces at its attachment point, a simple spring-mass system cannot be designed to provide a force-time characteristic to match, and oppose, a driving force which is only positive (or negative).
Thus the prior art related to vibration isolation systems employing the principle of the dynamic damper do not teach methods appropriate to damping, or isolating, non-sinusoidal or impulse -type driving forces. In general, then, none of the prior art in any related field teaches the principles disclosed in this invention.